"We've still got a small chance of winning the competition, " said Boks skipper Victor Matfield.
We were working the big Boks forwards around and it became a soft platform after that.
Giteau's conversion saw the Boks staring at a 17-point deficit going into the final quarter.
Change slowly came, and under new captain Gary Teichmann the Boks embarked on a record-breaking 17-game winning run.
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But Steyn's 38th-minute try regained the lead the Boks never relinquished as four further penalties secured the win.
Tries from Wikus van Heerden and Breyton Paulse helped the Boks into a surprise 17-0 lead in Sydney.
Saturday's win ensured the tourists avoided the ignominy of a first series whitewash by the Boks in 118 year.
But Schalk Burger is absent as he will miss the Boks' first three games after being banned for eye-gouging.
Wales were at the height of Henry-mania when they next faced the Boks.
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However, with a minute left the Emerging Boks kicked a penalty to the corner and won the resulting line-out.
The Scots have not scored a home try for 14 months and have not beaten the Boks since 2002.
But a minute from the break, Rocky Elsom stole ball at a Springboks line-out and stormed into the Boks' 22.
In a remarkable performance the men in red tore into the Boks.
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Hougaard landed the conversion and then added a penalty when Sharpe was caught offside to give the second-string Boks a shock 17-0 lead.
White took charge of the Boks in 2004 and oversaw a stunning transformation in their fortunes, leading them to the Tri-Nations title that year.
The Boks enjoyed territorial dominance as the half wore on but the US defended bravely and even trimmed the gap through a Hercus penalty.
Jake White, if you recall, coached Burger and the Baby Boks to Junior World Cup success before masterminding South Africa's senior side to world domination.
"Tami was in great form, her tenacity at the breakdown will be missed, " said Boks coach Denver Wannies who has named Pulane Motloung as a replacement.
Captain Mandisa Williams is one of nine members of the Boks squad from their last World Cup campaign, while Natasha Hoffmeester was kept out by injury.
Mike Phillips is the favourite to start at scrum-half but Blair's ability to make darting breaks around the side of the breakdown will scare the Boks.
Coach Peter de Villiers just seems to be there as a figurehead and I really don't know how much input he is having with the Boks.
But after Giteau was harshly penalised for a forward pass, the Boks made the most of their superb field position to open the scoring with a close-range try from Van Heerden.
Scotland's other big problem will be trying to contain the threat of the Boks' rampaging back row because if you stop them you nullify a lot of what South Africa are about.
However, Habana gathered his own clever chip down the left to score two minutes later when Gonzalo Olongo lost the ball in the tackle and the Boks pounced on the counter attack.
Roared on by a vocal 27, 000 crowd, Mark Taylor and Gareth Thomas claimed the tries that helped overwhelm the dispirited Boks, giving Wales their first ever victory over the giants of the game.
BBC: SPORT | Rugby Union | Internationals | Mighty Boks: South African rugby
They've got a huge pack and are physical with it, the Boks can front up to any pack in the world and if we do not get a forward platform we will be lost.
BBC: South Africa are probably the best in the world at the moment
Williams and Fitzgerald both produced sharp breaks early on, with the Emerging Boks seemingly unnerved by the Lions' aggressive blitz defence as they struggled to play the fluent game promised by their coach Dick Muir.
Coach Marcelo Loffreda was sending out contradictory signals about his side this week, claiming he was in charge of the strongest squad fielded by Argentina while dismissing their chances of beating the Boks for the first time.
Giteau punished some Boks foul play with a penalty in the ninth minute before Robinson scored the opening try just before the half-hour, the video referee adjudging the prop had grounded the ball despite Jean de Villiers' tackle.
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